Note that in accordance with relation (67) [1]}, we have
\((V^{^{\!-\!1}}\!\!f,f)_{\mathfrak {H}} =2( S H^{ \frac{1}{2}}f,H^ \frac{1 }{2}f)_{\mathfrak {H}}\ge 2\Vert H^ \frac{1 }{2} f\Vert ^{2}_{\mathfrak {H}}=2(Hf,f)_{\mathfrak {H}} ,\,f\in \mathrm {D}(V^{^{\!-\!1}}),\) 
